The invention relates to a sensor system and a method for determining system states, referred to as states hereafter.
In systems, whose state variables are to be determined by means of at least one sensor of a sensor system with an associated arithmetic unit, the determination of these variables, which is as accurate as possible from at least one measurement per time point, is of great importance for the functioning capacity of the system. This applies particularly to systems that are critical to safety, for example, air data systems of an airplane, since with insufficient accuracy of the measured values, addition means such as, additional sensors, are necessary in order to achieve the required safety of the overall system. Additional examples are found in the determination of states for chemical and nuclear reactions or in navigation for the determination of position from several measurements that are input, such as GPS or radar systems.
In systems with sensor systems having at least one sensor and an arithmetic unit assigned to this sensor for determining at least one state variable of the system, methods are known, which assign a specific state variable to the measured value of the sensor, optionally as a function of other parameters of the system, by means of inverting a one-dimensional calibration curve of a sensor. For example, in the case of an air data system of an airplane, the measurement of the instantaneous flight state is conducted by means of air data sensors, which measure, for example, static and dynamic pressures in the vicinity of the fuselage. State variables of the undisturbed flow, such as, flow angle, Mach number, and dynamic pressure, are determined from these measured values by means of the one-dimensional inversion of the previously determined calibrations of the measurement as a function of a state, thus, for example, a pressure measurement as a function of static pressure.
It is a disadvantage of this method that the one-dimensional inversion of multidimensional calibrations permits only an imprecise determination of states. Stability problems may also occur.
Therefore, a method has been developed for an air data system, in which a determination of the instantaneous state variables x of the system is carried out from at least one sensor signal by means of a cost function c2 (x, y, u), which comprises calibration curves or surfaces, in order to optimize the precision and reliability of the states x to be determined. This method is disclosed, for example, in (Friehmelt H., Jost, M., Flush Air Data System-Advanced air data system for air and space travel, DGLR [German Association of Air and Space Travel], Annual conference 1999, Berlin, presentation 99–180, page 5). Calibration curves or surfaces of sensor signal y, which is generally a vector and is dependent on the sought state variable x and known configurations or inputs from controlling means u are used in this method.
In the case of the air data system, for which this method is proposed, x represents the air data a, b, qc and ps, y represents the pressure measurements, i.e., the measured values, and u represents airplane configurations, thus system-dependent parameters.
In order to determine the instantaneous state variables x in the proposed air data system, a minimization of the cost function c2 (x, y, u) is proposed by means of a gradient descent method. The cost function c2 (x0, y, u) is reduced starting from a randomly selected initialization x0 of the state through a recursive variation of x along the gradient of c2 until a local minimum of c2 with respect to x is obtained.
The disadvantage of this method is that several iteration cycles are necessary in order to obtain the global minimum, in which the computation time of the system is increased. It is also a disadvantage that the obtaining of a global minimum of c2 cannot be guaranteed. The described method is particularly disadvantageous in those cases in which the calibration surfaces can be a highly fractured. This occurs in an air data system, e.g., in transonic systems.